Emergent heavy fermion and superconductivity near Mott transition in twisted bilayer graphene

Abstract

Near a bandwidth-tuned Mott transition, the Fermi velocity $v_F$ and quasiparticle residue $Z$ of a metal often vanish. Here, we show that analogous phenomena emerge in twisted bilayer graphene (TBG) at integer fillings and can be captured by an emergent heavy-fermion framework within a projective active-band limit. Unlike models incorporating remote bands, our effective heavy-fermion description arises from \textit{mixed-valence Mott} physics via decoupled charge and local-moment sectors. In the charge sector, active bands $c(\mathbf{k})$ hybridize with an emergent \emph{orthogonal fermion} $ψ(\mathbf{k})$ to open a large Mott gap at $|\mathbf{k}| > k_*$ ($k_*$ sets the momentum-patch size) and a quadratic band-touching semimetal near $\mathbf{k}=0$ at neutrality ($ν=0$). The orthogonal fermion is a linear combination of the doublon and holon excitations and may be written as $ψ_i \sim (δn^f_i+\frac{1}{2})^{-1} f_i$. An emergent Kondo coupling $J_K \sim U$ ($U$ is the local Hubbard interaction) between $ψ$ and local moments $ψ'$ frames the Mott transition as a Kondo screening transition, tuned by the twist angle $θ$. Away from the magic angle, a Kondo-screened heavy semimetal develops below $T_K$ (the Kondo temperature) with vanishing $Z$. Introducing anti-Hund's coupling $J_A$ generates an s-wave fully gapped or nematic, nodally gapped superconducting dome near the Mott boundary even at $ν=0$. At other integer fillings $ν= \pm 1, \pm 2$, increasing bandwidth first drives the small-gap Mott state into an intermediate quadratic band-touching semimetal before entering a heavy Fermi liquid with large Fermi surfaces. Our results establish a unified framework for emergent heavy fermion physics with both itinerant carriers and local moments from the $f$ orbital.